...Test for Normality in Stock Return
Abstract
The objective of the first assignment is to determine if TJX’s stock returns are normally distributed. We pulled pricing data from 899 days before the corporate data breach and 100 days after the event and then conducted several tests in order to draw a conclusion about the distribution of TJX’s returns. The KS test for the 1,000 observations suggested TJX’s stock returns are not normally distributed. The F test suggested that the volatility of at least two samples is significantly different. We conclude that returns of TJX are not normally distributed.
Introduction
Normal distribution is one of the most important statistical distributions as it is used to draw conclusions from sample data about the populations from which theses samples are drawn from. This distribution also has some important characteristics, such as the normal distribution is symmetrical about its mean. Also, the normal distribution provides a benchmark of how the data is dispersed; the normal distribution states that 99.73% of the probability density function lies within three standard deviation of the mean. The test of normality will help analyze other statistical feature of TJX’s stock return.
Method
In our analysis, we conducted a KS test to determine if the total number of observations was drawn from a normal distribution firstly. Then we took the 1,000 observations and broke them into subsets to test if these smaller samples were normally...

...INTRODUCTORY ECONOMETRICS
Lectures 1 & 2
Statistics for Econometrics
POPULATION AND SAMPLE
Population – the group of ALL people or objects that are
under study
Sample – a sub-set of the population
Parameter – a numerical characteristic of a population
1. Population & Sample Means
2. Expected Values
3. Population & Sample Variances
4. Population & Sample Covariances
5. Population & Sample Correlation Coefficients
6. Estimators
Statistic – a numerical characteristic of a sample
Statistical inference – drawing conclusion about a
population based on information contained in a sample
Random sample – every sample of the same size in the
population has the same chance of being selected
1
2
POPULATION MEAN AND SAMPLE MEAN
Set of all possible values of a random
variable X
Parameters: population mean µ
2
population variance σ X
Given a random variable X (e.g. IQ scores, weights of all
students, salaries of all workers, outcomes from tossing a die)
We consider a random sample of size n
the sample containing n observations of X denoted by
x1 , x2 , x3 ....,xn
Sample mean = X =
Take many
random samples
of size n
1 n
∑ xi
n i =1
Population mean of X =
µ
For each random sample of size n
drawn from the population,
Statistics: sample mean
X
sample variance s 2
= E(X )
X
More on expected values later…
3
Set of all possible values X
…follows a normal distribution, if there are...

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ECONOMETRICS
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First of all, I would like to apologize for showing the results in Spanish, but I couldn’t find the way to change Gretl’s language. However, all the explanations are in English, so I hope there is no problem to understand the results.
Secondly, I would just inform you that the time-series data that I have used is “U.S. macro data, 1950-2000” from Greene Sample folder in Gretl.
Before building the model…
I would try to explain the variable “Real GDP” using the variables “Real consumption expenditures”, “Real Private-Sector Investment”, “Real government expenditure”, “Unemployment rate” and “Inflation rate”. To do so, the first thing we should do is to check if there is correlation risk between the independent variables. We will use the Correlation Matrix to figure out this:
Since the coefficient of correlation between the variables Real Consumption, Real Private-Sector Investment and Real Government expenditure is very close to 1, it means that those variables are providing almost the same information, so I would delete some of them, and check the coefficient of correlation again.
Once Real Private-Sector investment and Real Government Expenditure have been deleted from the correlation matrix, the coefficients of correlations between variables are acceptable now, and we can be sure that every variable gives different information about the model.
However, I could have also used another statistic to check is...